11 Pages

Hardcopy

Course: CS 3600, Fall 2009
School: CSU Stanislaus
Rating:
 
 
 
 
 

Word Count: 4612

Document Preview

16: Chapter Hardcopy Introduction You have worked hard to analyze a problem and have developed really good models and great images or animations that communicate your solution to that problem, but those images and animations only run on your computer and are presented on your screen. Now you need to take that work and present it to a larger audience, and you dont want to lose the control over the quality of your...

Register Now

Unformatted Document Excerpt

Coursehero >> California >> CSU Stanislaus >> CS 3600

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
16: Chapter Hardcopy Introduction You have worked hard to analyze a problem and have developed really good models and great images or animations that communicate your solution to that problem, but those images and animations only run on your computer and are presented on your screen. Now you need to take that work and present it to a larger audience, and you dont want to lose the control over the quality of your work when you take it to a medium beyond the screen. This work may used as part of something that will be used by others, or it may be something you want to save as part of an archive you will create. In this chapter we talk about the issues you will face when you do this. We will discuss different technologies for different kinds of computer graphics work, including digital and print images, film and video, and 3D object prototyping for creating physical images of computer models. When you have worked through this chapter, you should have a good idea of the appropriate kind of hardcopy for your work and the application for which it will be used, and should understand some of the questions about how to create this hardcopy. In order to make the best use of the information in this chapter, you need an understanding of the nature of color and visual communication, an appreciation of what makes an effective image, and an idea of the wide range of ways that people can use computer graphics results. Definitions Computer graphics hardcopy is output in a fixed medium that can be taken away from the context in which it was created, and can be communicated to your audience without that original context. There are several ways this can be done, but the basic idea is that any kind of medium that can carry an image is a candidate for hardcopy. These can be physical (paper, sculptural) or digital (images, video). Each of these media has its own issues in terms of its capability and how you must prepare your images for the medium. In this chapter we will discuss some of the more common hardcopy media and give you an idea of what you must do to use each effectively. Creating hardcopy can mean creating a digital record of the work that can be sent to some sort of output device. That device may be actually attached to the computer, such as a printer or a film recorder, or it may be a device to which we communicate data by network, disk, or CD-ROM. So part of the discussion of graphics hardcopy will include a description of the way data must be organized in order to communicate with external production processes. Digital images: If your work creates single images, then one way to communicate these images is by saving them to a file that is organized by some generally-readable graphics file format. We have seen in earlier chapters that we can save the contents of our color buffer into an internal color array, and this array can be processed to create an image file in any of the alphabet soup of standard formatsGIF, TIFF, JPEG, PNG, or others. If you simply write the array to a file of unsigned characters, you will create what is sometimes called a raw RGB file, and there are generally-available libraries of tools for format conversion that can translate such files into the more generally useable formats above. If you do not have a library of file format conversions around, then you can open a raw RGB file with Photoshop and save it with any of the standard formats; in essence you are using Photoshop as a file format conversion utility. If you are not familiar with these file formats, perhaps a quick description is in order. GIF stands for Graphics Image Format, and it stores images in 8-bit indexed color with some lossless compression. However, the GIF file format involves Lempel-Ziv-Welch (LZW) file compression, and this is a patented process so you must license it if you create any software that implements this algorithm. TIFF is the Tagged Image File Format, a very general format that stores images with whatever color depth you need. Generally there is little file compression with TIFF files and they can be very large, but the format is generally lossless and so is a good archival format (especially since disk or CD-R space is quite inexpensive). JPEG is a file format that often uses a lossy compression based on the discrete cosine transformation, but it can be lossless if you choose. JPEG is strong on natural images but weak on images that have lines or sharp edges because the discrete cosine transformation operates on 64x64 blocks of pixels and can distribute the edge information around a pixel block. Its name is based on its developers: the Joint Photographic Experts Group. PNG stands for Portable Network Graphics, a file format that was created in an effort to replace GIF as a widely-used format for images on the networks. One of the main aspects of PNG is that it does not use any legally encumbered data compression. It includes the capabilities of GIF but adds full-color support, including alpha values, as well as 16-bit grayscale support. Print: One version of printed hardcopy is created by a standard color printer that you can use with your computer system. Because these printers put color on paper, they are usually CMYK devices, as we talked about in the color chapter, but the printer driver will usually handle the conversion from RGB to CMYK for you. In order of increasing print quality, the technologies for color output are inkjet, where small dots of colored ink are shot onto paper and you have to deal with dot spread and over-wetting paper as the ink is absorbed into the paper, wax transfer, where wax sticks of the appropriate colors are melted and a thin film of wax is put onto the paper, and dye sublimation, where sheets of dye-saturated material are used to transfer dyes to the paper. These devices have various levels of resolution, but in general each has resolution somewhat less than a computer screen. All these technologies can also be used to produce overhead foils for those times when you have only an overhead projector to present your work to your audience. Figure 16.1: separations for color printing 2/18/03 Page 16.2 Print can also mean producing documents by standard printing presses. This kind of print has some remarkably complex issues in reproducing color images. Because print is a transmissive or subtractive medium, you must convert your original RGB work to CMYK color before beginning to develop printed materials. You will also need to work with printing processes, so someone must make plates of your work for the press, and this involves creating separations as shown in Figure 16.1 (which was also shown in the chapter on color). In the most widely-used color reproduction technology, plate separations are created by masking the individual C, M, Y, and K color rasters with a screen that is laid across the image at a different angle for each color; the resulting print allows each of the color inks to lay on the paper with minimal interference with the other colors. A screen is shown, greatly enlarged, in Figure 16.2, where the enlargement is so great that you can see the angles of the screens for the C, M, Y, and K components. (You should look at a color image in print to see the tell-tale rosettes of standard separations.) There are other separation technologies, called stochastic separations, that dither individual dots of ink to provide more colored ink on the page and sharper images without interference, but these have not caught on with much of the printing world. Creating separations for color-critical images is something of an art form, and it is strongly suggested that you insist on high-quality color proofs of your work. You must also plan for a lower resolution in print than in your original image because the technologies of platemaking and presses do not allow presses to provide a very high resolution on paper. Figure 16.2: C, M, Y, and K screens in a color image, greatly enlarged There are other technologies for creating color print images, including one called stochastic screening (sometimes called FM color) that produces color for small areas of the paper that moves the amount and placement of the color algorithmically to produce higher color resolutions and better color saturation than the standard screen techniques described above. This technology has been available since the early 1990s in selected print shops and has been used for a wide variety of printing. However, it is not widely used and you may have difficulty finding examples of this kind of separation. Film: Sometimes you want to present the highest-quality images you can to an audience: the most saturated colors and the highest resolution. Sometimes you want to be sure you can present your work without relying on computer projection technology. In both cases, you want to consider standard photographic images from digital film recorders. These are devices that generate images 2/18/03 Page 16.3 using a very high-quality grayscale monitor, a color wheel, and a camera body and that work with whatever kind of film you want (usually slide film: Kodachrome, Ektachrome, or the like). A film recorder is organized as shown in Figure 16.3. The grayscale monitor generates the images for each color separately, and that image is photographed through a color wheel that provides the color for the image. Because a grayscale monitor does not need to have a shadow mask to separate the phosphors for different colors, and because the monitor can be designed to have a long neck and small screen to allow for extremely tight control of the electron beam, it can have extraordinary resolution; 8K line resolution is pretty standard and you can get film recorders with up to 32K lines. This allows you to generate your image at resolutions that would be impossible on the screen. Figure 16.3: schematic of digital film recorder Film is much less of a problem than print, because you can work directly with the image and do not need to deal with separations, and you work with the usual RGB color model. Recall that slides produce their image by having light projected through them, so they behave as if they were an emissive medium like the screen. Your only issue is to deal with the resolution of the camera or to accept the interpolations the film recorder will use if you dont provide enough resolution. Video: Video can be a very important medium for your animated computer graphics work, because it is the only medium available to show the motion that is so important to communicate many of your ideas. At the same time, it can be one of the most limited media available to you, at least until video leaves the early 20th century and really comes into the 21st century. We will focus on NTSC video here, but there are similar issues for PAL or SECAM video, and if you are reading this in one of the areas where PAL or SECAM are the standards, you should check to see how much the comments here apply to you. There are some important issues in dealing with video. The first is resolution: the resolution of NTSC video is much lower than even a minimal computer resolution. NTSC standards call for 525 interlaced horizontal scan lines, of which 480 are visible, so your planned resolution should be about 640 by 480. However, many television sets have adjustment issues so you should not ever work right against the edge of this space. The interlaced scan means that only half of the horizontal lines will be displayed every 1/30 second, so you should avoid using single-pixel horizontal elements to avoid flicker; many television sets have poorly-converged color, so you should also avoid using single-pixel vertical elements to they will not bleed into each other. In fact, you will have the best results for video if you design your work assuming that you have only half the resolution noted above. 2/18/03 Page 16.4 A second issue in video is the color gamut. Instead of being composed of RGB components, the NTSC television standard is made up of significant compromises to account for limited broadcasting bandwidth and the need to be compatible with black-and-white television (the NTSC standard dates from the late 1930s, before the wide-spread advent of color television or the advent of modern electronics and other technology). The NTSC color standard is a three-component model called the YIQ standard, but the three components are entirely focused on video issues. The Y component is the luminance (or brightness), and it gets most of the bandwidth of the signal. The I component is an orange-to-blue component, and it gets a little more than 1/3 of bandwidth of the Y component. The Q component is a purple-to-green component, and it gets a little more than 1/3 of the I component. The best color you can get in video always seems to be under-saturated, because that is part of the compromise of dealing with the technology available. To be more precise, the following table shows the bandwidth and the horizontal resolution for each of the components of the video image: Component Y I Q Bandwidth 4.0 Mhz 1.5 Mhz 0.6 Mhz Resolution/scanline 267 96 35 In order to get the best possible horizontal resolution from your image, then, you need to be sure that the elements that vary across the line have differing luminance, and you should focus more on the orange-to-blue component than on the purple-to-green component. If you want to understand how your colors vary in YIQ, the following conversion matrix should help you evaluate your image for video: |Y| | 0.299 0.587 0.114 | |R| |I| = | 0.596 -0.275 -0.321 | |G| |Q| | 0.212 -0.528 0.311 | |B| The question of video is complicated by the various digital video such formats, as QuickTime and MPEG, that require computer mediation to be played back. Digital video is RGB, so it does not have many of the problems of NTSC until it is actually played on a television screen, and there are television sets that will handle increasingly-high quality video. In fact, MPEG II is the video standard for DVD, and there are self-contained DVD players, so this provides one alternative to doing your own conversion to NTSC. Figure 16.4: screen capture of an NTSC video image. Note the relatively low resolution and limited colors. 2/18/03 Page 16.5 In the longer term, television will be moving to computer-compatible native digital formats and the high-definition television (HDTV) standards will support direct RGB color and higher-resolution, non-interlaced images, so we look forward to this discussion becoming antiquated. For the time being, however, you may need to put up with creating images that will make your graphics colleagues ask, That looks terrible! Why are you doing that? Figure 16.4 is a photograph of a video image that shows the problems with color and resolution. If they understand that youre going to video, however, theyll understand. Digital video: Creating a digital video from an animation is straightforward with the right tools. If you are creating an animation, for example, you may generate a single frame of the animation in a window on the screen and then use a function such as we described in earlier chapters to save the contents of the window to an array, which can then be written to an image file, possibly with a name that represents the frame number of that image in the overall animation. After you have completed running your set of animation segments, and have created the set of individual frames, you may import them into any of a number of tools that will allow you to save them as a digital movie in QuickTime or MPEG format. There are several levels of MPEG format, with each level having a higher compression than its predecessor. Many of these tools will also allow you to add a sound track, do transitions from one animation sequence to another, or add subtitles or other text information to the movie. And when you finish developing the video, you can write it to a CD-R or even DVD-R disk to share with others. 3D object prototyping: There are times when having an image of an object simply isnt enough, when you need to be able to run your fingers over the object to understand its shape, when you need to hold two objects together to see how they fit, or when you need to see how something is shaped so you can see how it could be manufactured. This kind of 3D object prototyping is sometimes called 3D printing and is done by special tools. You can view the resulting object as a prototype of a later manufactured object, or you can view it as a solid representation of your graphic image. Figures 16.5 through 16.8 show photographs of the (3,4)-torus, introduced in the chapter on graphics for the sciences, as created by several of these 3D printing techniques, as noted in the figure caption. The contact information for each of the companies whose products were used for these hardcopies is given at the end of the chapter. There are, of course, other older technologies for 3D hardcopy that involve creating a tool path for a cutting tool in a numerical milling machine and similar techniques, but these go beyond the prototyping level. There are several kinds of technologies for creating these prototype objects, but most work by building up a solid model in layers, with each layer controlled by a computation of the boundary of the solid at each horizontal cutting plane. These boundaries are computed from information on the faces that bound the object as represented in information presented to the production device. The current technologies for doing such production include the following: The Helisys LOM (Laminated Object Manufacturing) system lays down single sheets of adhesive-backed paper and cuts the outline of each layer with a laser. The portion of the sheets that is outside the object is scored so that the scrap to be removed (carefully!) with simple tools, and the final object is lacquered to make it stronger. It is not possible to build objects that have thin openings to the outside because the scrap cannot be removed from the internal volumes. LOM objects are vulnerable to damage on any edges, especially those at the very top or bottom of the layers, but in general they are quite sturdy. Figure 16.5a shows the torus created with the LOM system; note the rectangular grid on the surface made by the edges of the scrap scoring, the moir pattern formed by the burned edges of the individual 2/18/03 Page 16.6 layers of paper in the object, and the shiny surface is made when the object is lacquered to preserve it from handling and other use. Figure 16.5: the torus created by the LOM system The Z-Corp Z-402 system lays down a thin layer of starch powder and puts a liquid binder (in the most recent release, the binder can have several different colors) on the part of the powder that is to be retained by the layer. The resulting object is quite fragile but is treated with a penetrating liquid such as liquid wax or a SuperGlue to stabilize it. Objects built with a wax treatment are somewhat fragile, but objects built with SuperGlue are very strong. Because the parts of the original object that are not treated with binder are a simple powder, it is possible to create objects with small openings and internal voids with this technology. Figure 16.6 shows the torus created with the LOM system; note the very matte surface that is characteristic of objects created by powder composition of the object. Figure 16.6: the torus created by the Z-Corp system 2/18/03 Page 16.7 The 3D Systems ThermaJet system builds a part by injecting a layer of liquid wax for each layer of the object. Such parts must include a support structure for any regions that overhang the objects base or another part of the object, and this support can either be designed when the object is designed or provided automatically by the ThermaJet system. Because the object is made of wax it is not stable in heat, is not very strong, and is subject to breakage on any sharp edges. The need for a support structure makes it difficult to include voids with small openings to the outside. Also because of the support structure, the bottom part of an object needs to be finished by removing the structure and smoothing the surface from which this was removed. Figure 16.7 shows the torus as created by the ThermaJet system; note the slightly shiny surface of the wax in the object. The color depends on the color of the available wax; other colors besides gray are possible. Figure 16.7: the torus created by the 3D Systems ThermaJet system The 3D Systems stereolithography system creates an object by building up thin layers of a polymer liquid and hardening the part of that layer that is to be retained by scanning it with a laser beam. As with the ThermaJet system, this requires a very solid support structure for parts of the object, particularly because there is a small contraction of the polymer material when it is treated with the laser. The support structure must be removed from the object after it is completed, so some finishing work is needed to get fully-developed surfaces. The polymer liquid can readily be drained from any interior spaces if there is an opening to the outside, so this technology handles non-convex objects well. The polymer is very strong after it is hardened after the shaping is complete, so objects created with this technology are very sturdy. Figure 16.8 shows the torus as created by the stereolithography system. One common issue for 3D prototyping systems is the durability of the objects they create. Some of the technologies produce very durable objects; the polymer material for stereolithography is very strong, and a powder-based object stabilized with a super glue liquid can even handle someone standing on it. Other technologies, such as wax deposition or powder buildup stabilized with wax, are quite fragile. Your choice of technology will depend on j...

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

IUPUI - M - 221
October 1, 2007 MATH 221 Sample FINAL EXAM Problems SHOW YOUR WORK, PLEASE Problem 1 Find: a. lim x2 - 3 x 5 - 2x2x2 - 3 b. lim x4 5 - 2x2c. limx2 - 5x + 6 x2 x2 + x - 6Problem 2 Use the definition (in other words, use the delta-process or th
IUPUI - STAT - 113
Observational VS. Experimental StudiesExperiments, Experiments Good and BadObservational Studies are passive data collectionObserve, record & measure Don't Interfere!Chapter 5Experiments are active data production p pActively intervene by i
IUPUI - HW - 9
Characterizing Tumor Motion Using 4-D Computed TomographyStudent : Huanmei Wu (NU) Contributors: Eike Rietzel (MGH), George Chen (MGH), David Kaeli (NU), Betty Salzberg (NU)AbstractThe general objective of radiotherapy is to achieve tumor control
IUPUI - LL - 7
ECE 302: Probabilistic Methods in Electrical Engineering Fall 2008: HW 1 SolutionProblem 1. Let set A = {4, 5, 7, 9}, set B = {2, 4, 3, 7}, the universal set S = {1, 2, 3, 4, 5, 6, 7, 8, 9}. 1. What is the set of elements in A B?Solution: The unio
IUPUI - CPT - 499
C 499 I nte t S for Educators PT rne killsS ssion S e ix Class Note sC 499 I nte t S for Educators PT rne killsInternet Services Electronic Mail Bulletin Board Service File Transfer Remote Login Browsing the WWW Gopher WAIS (Wide Area Informatio
IUPUI - CPT - 499
C 499 I nte t S for Educators PT rne killsOve w of theI nte t rvie rne S ssion One eObjectivesDe scribetheI nte t and its history; and rne e xplain how to acce theI nte t ss rne De scribetheWWW in conte of hype xt and xt rte hype e rm dia Distin
IUPUI - CPT - 499
C 499 I nte t S for Educators PT rne killsC Note lass s S ssion S ve e e e nte n http:/digischool.bart.nl/e rsie dalton1.htm ngve /e http:/e b.gsn.org/ dwe http:/m nnium d.org/ ille .ae http:/www.whatuse k.com e /cgi-bin/re ct.go?url dire =htt
IUPUI - CPT - 499
C 499 I nte t S for Educators PT rne killsS ssion Eight & Nine e C Note lass sWorld WideWe bTheWorld WideWe [WWW or theWe is a subse b b] t of theInte t S mthat pe its thelinking of rne yste rm m ultim dia docum nts am se rs on theI nte t e e on
IUPUI - BENEDICT - 2007
p=headline foo here%2E%2E%2E%7Cundefined undefined%7Cundefined%7CPhotographs by James W%2E Brown%2C Executive Associate Dean%7Cabstract here%2E%2E%2E&m=undefined%7Cundefined%7C0%7C1%7C1%7C140937%7CFFFFFF%7C000000&n=version%7C295%5Eheadline%7Cheadline
CSU Stanislaus - CR - 6
California State UniverSity, StaniSlaUS Inventory of ConCurrent ACCredItAtIon And Key PerformAnCe IndICAtors WAsC dAtA exhIbIt 8.12008 Name of accredited or certificated programArtProfessional, special, state, or programmatic accreditations curre
CSU Stanislaus - CR - 1
California State University, Stanislaus[CORE INDICATOR 1: QUALITY OF PROGRAMS]Graduating Senior Survey 2004/05,2005/06, and 2006/07Overall Evaluation of CSU StanislausThe CSU Stanislaus Graduating Senior Survey asks graduating seniors with sev
CSU Stanislaus - CR - 6
PRePARAtion/SeleCtion levelS oF enteRing StudentS WASC dAtA exhibit 1.22008 Fall 2002NEW FRESHMEN SAT Scores Verbal Quantitative ACT Scores Composite Mathematics English NaturalSciences SocialStudies Other Tests Used TOEFL* Paper-basedTest Compu
CSU Channel Islands - MATH - 140
Math 140 Final Review Tuesday December 9, 4:00-6:00 for the 4:30 class Thursday December 11, 7:00-9:00 for the 6:00 class The nal will be comprehensive over the material in class. This review is designed to be an aid in study for the nal. It is not d
CSU Channel Islands - MATH - 95
Midterm 1 Review Sheet Solutions1. a. Find the equation of the line passing through the points (1, 2) and (3, 4). b. Sketch the graph of this line. Solution. a. The slope is given by m= 42 1 = , 3 (1) 2so we can use the point-slope formula with t
CSU Channel Islands - MATH - 140
Math 140 Midterm 1 Review Solutions 1. The resulting graph is shifted right by 2, reected across the x-axis, and then raised by 1. 2. Remember when sketching that on the dierent pieces of the domain, the dierent rules take eect. So when x < 2, the gr
CSU Channel Islands - MATH - 140
Math 140 Midterm 1 Review Midterm 1 - Thursday Oct. 2 The midterm will cover the sections we covered 1.1-2.3. This review is designed to be an aid in study for the midterm. It is not designed to mimic exactly what will be on the exam. The problems on
CSU Channel Islands - MATH - 140
Math 140 Midterm 1 Review Midterm 1 - Wednesday March 5 The midterm will cover the sections we covered 1.1-3.2. This review is designed to be an aid in study for the midterm. It is not designed to mimic exactly what will be on the exam. The problems
CSU Channel Islands - MATH - 140
iV{arn 140 lVltorpnu 2Nor,'ttrttun 6 Ttttrttso.,rl'Ntltrtt: ( 'illlrV^ r-'(-lb ?o$t'l'lrcru:; r t , , , . r r i , , i .l , , , , i r r l i t i . l i r r i , ' , ' . i , r l r r $ i , , , i l t t : . : r i j r i 1 l , , i r ' o t r t t ' l r i
CSU Channel Islands - MATH - 140
Math 140 Midterm 1 Review Solutions 1. The resulting graph is shifted right by 2, reected across the x-axis, and then raised by 1. 2. Remember when sketching that on the dierent pieces of the domain, the dierent rules take eect. So when x < 2, the gr
CSU Channel Islands - MATH - 95
Midterm 1 Review SheetThis is a collection of exercises which are based upon the material we covered in class. This should not be taken as an implication that these problems look like those which will be on the midterm. The concepts they embody, how
CSU Channel Islands - MATH - 140
Math 140 Midterm 2 Review Midterm 2 - Thursday November 6 The midterm will cover the sections 3.1-3.6. This review is designed to be an aid in study for the midterm. It is not designed to mimic exactly what will be on the exam. The problems on the ex
CSU Channel Islands - MATH - 140
Math 140 Midterm 2 Review Problem Solutions Problem solutions. 1. Let g(x) = 2x2 4x + 7. What is the average rate of change of g(x) between x = 1 and x = 4? The average rate of change is the change in g divided by the change in x. So we have that th
CSU Channel Islands - MATH - 140
Math 140 Final Review Solutions Monday May 12 1:00-3:00 for 12:00 class Friday May 16 4:00-6:00 for 3:00 class The first 36 exercises are adapted from the reviews for midterms 1 and 2; for the most part, just the numbers are changed. Details on how t
CSU Channel Islands - MATH - 140
Math 140 Midterm 2 Review Problem Solutions Problem solutions. 1. Using the properties of limits, findx3lim4x + 4 = = = x3lim (4x + 4)x3 x3 x3( lim 4)( lim x) + lim 4 43+4=4 x2 - 9 . x-32. Consider the function f (x) =(a) Using the
CSU Channel Islands - MATH - 331
224 1 224 Professor Roybal History of Mathematics 10/21/08 History of Mathematics Project 1This is an example of corresponding angles. In the diagram, the two horizontal lines are parallel to each other, and are crossed by a sloping straight line,
CSU Channel Islands - MATH - 331
History of Math Number: 369Math 331Project 1- Proofs GaloreA proof is a combination of statements and ideas that can be put together to prove a mathematical idea. Proofs can be long and complicated, but sometimes they are not nearly so long or c
CSU Channel Islands - MATH - 331
Math 331 ID# 268 Project 1 A proof is an ingenious way of solving difficult problems with simple algebra and geometry. You take a hard problem for example: 13 + 23 + . + n3 = (1 + 2 + . + n)2, and solve it using basic algebraic functions such as mult
CSU Channel Islands - MATH - 331
Math # 303 Proof: Proofs are used to help solve problems by taking step-by-step procedures. Each step is taken to show the reason why the answer for the problem is what it is. A proof illustrates why a problem would come to the conclusion that it doe
CSU Channel Islands - MATH - 331
Sam Levison 000296128 October 19, 2008 Math 331 Project #1Since humans in the 21st century where born they have always been taught the fundamentals of mathematics. As young children before any organized education we have been able to tell who has m
CSU Channel Islands - MATH - 331
314 Project1 Theconceptbehindaproofisthatwearetryingtoshowandvalidatea statementusingthecharacteristicsanddefinitionsofelementsrelatedtothe conceptwewanttoconfirm.Wethenmanipulatethosedefinitionsand characteristicsusingdeductivereasoning,untilweare
CSU Channel Islands - MATH - 331
Katie Gills Automathography!Hi Math 331 Classmates! So I have to admit, Math is not really my strong suit. I struggled with Math all through High School. Although back in Elementary school I liked it. Anyway, I always seemed to have really awesome
CSU Channel Islands - MATH - 331
MelanieHerrmannsAutomathography Istartedmathinkindergartenlikeeveryotheranklebiterandhave beenbadatitsincedayone.Icouldntreallytellyouwhy,itcomes easytosomepeopleandothers,likeme,arestuckbashingtheirbrainsin tryingtodothosetimedmultiplicationpages
CSU Channel Islands - MATH - 140
Math 140 Final Review Solutions Tuesday Dec. 9 4:00-6:00 for 4:30 class Thursday 7:00-9:00 for 6:00 class 1. Find all local and absolute minima/maxima for the function f (x) = x2 x . +9This function is dierentiable everywhere and has domain all of
CSU Channel Islands - MATH - 331
Project 1, History of math History of math number 167 A proof, is a demonstration that some statement logically follows from the definitions and axioms ("givens") of the world in question. For example, to prove that 1+1 <> 1 [1+1 is not equal 1] one
CSU Channel Islands - MATH - 331
Hello fellow Math 331 classmates. My name is Laura Cordero and I am currently taking my last two classes in order to graduate with my business degree. The only other math class I have taken here at CSU Channel Islands was Statistics. I have alwa
CSU Channel Islands - MATH - 331
Shahab Lashkari's AutomathographyGrowing up, I have always liked Math. Having been into computer programming since elementary school, I used Math and Logic quite often. I liked being able to describe things mathematically, and grew up experimenting
CSU Channel Islands - MATH - 331
(On vacation in Sonoma Jack London State Historical Park)Kims Authomathography Well, back in the covered wagon days when I went to high school, Algebra was not a requirement for graduation, and as a habitual D student in math, in my infinite wisdo
CSU Channel Islands - MATH - 331
Bryan Podgorny Project #1 Math 331 Due: 3/26/08Proof Explain in clear, ordinary language the concept of proof. A proof is a detailed and organized way to show that something is true or a fact. The way to show that something is true is to compare i
CSU Channel Islands - MATH - 331
Project 1: Proof and Greek Mathematics A proof is merely a justification for a conclusion, showing how the conclusion was obtained using logically true statements as steps. A proof can use deductive reasoning or inductive reasoning to obtain the conc
CSU Channel Islands - MATH - 331
#406 Math 331 Roybal 3/26/08Project 1What is the purpose of a proof? In mathematics a proof is used to prove a problems solution to be true; its made up of steps that are specifically used to come to a conclusion. But to a non-mathematician, a pro
CSU Channel Islands - MATH - 331
History of Math # 415 03/24/2008 Math 331 History of MathematicsA proof is a use of known theorems and basic algebra to show through a logical succession of steps that a mathematical problem is either true or false. Basically you start with a math
CSU Channel Islands - MATH - 331
280 Dr. Richard Roybal Math 331 24 March 2008 The Mathematical Proof Math is unique in many ways but one thing that makes it extremely unique is that it can also be categorized as a language. A language is usually defined as a tool that it is used to
CSU Channel Islands - MATH - 331
Project 1 #971 Q.E.D. Does not Stand for Quite Easily DemonstratedIn order to completely understand mathematics, you must understand the method of using proofs. Proof-based mathematics is paramount in providing evidence for a certain theorem or rul
CSU Channel Islands - MATH - 331
Project1-370 March 26, 2008 Proofs Why? As children, it was the one question we were really good at asking. Whysomething was the way it was. Children want to know the essence of an object and understand its existence. Conceptually, proofs work in
CSU Channel Islands - MATH - 140
Math 140 Final Review Monday May 12 1:00-3:00 for 12:00 class Friday May 16 4:00-6:00 for 3:00 class The final will be comprehensive over the material in class. This review is designed to be an aid in study for the final. It is not designed to mimic
CSU Channel Islands - MATH - 331
Stacys automathographyI love numbers. Math is my favorite subject; it always has been and always will be. When I was in elementary school I always did well in Math. In the second grade my entire class made number scrolls. We were each given paper of
CSU Channel Islands - MATH - 140
Math 140 Midterm 2 Review Midterm 2 - Wednesday April 9 The midterm will cover the sections 3.1-3.6. This review is designed to be an aid in study for the midterm. It is not designed to mimic exactly what will be on the exam. The problems on the exam
CSU Channel Islands - MATH - 208
Math 208: Reective Writing Assignment 1 Mathematizing is solving problems, posing problems, playing with patterns and relationships, and proving their thinking to fellow mathematicians. We constantly mathematize physical and social phenomena and use
CSU Channel Islands - MATH - 208
Math 208: Reflective Writing Assignment 2 From Alternate Algorithms by Michael Naylor: Learning a variety of algorithms that focus on number sense will help kids develop a better understanding of number operations. An algorithm is a step-by-step "rec
CSU Channel Islands - MATH - 140
CSU Channel Islands - MATH - 208
Math 208 Review 21. Dene the following terms: prime number, composite number. Which positive integer is neither prime nor composite? 2. Use the Sieve of Erastothenes to nd all the primes up to 200. (You may start sieving at 101, if you desire so.) 3
CSU Channel Islands - MATH - 208
Math 208, First Exam Review 1. What are the four steps to Polyas problem solving process? 2. What are some problem solving strategies? 3. Show why 3 always divides evenly into the sum of any three consecutive whole numbers. (Hint: What are the possib
CSU Channel Islands - MATH - 140
CSU Channel Islands - MATH - 331
The concept of "proof" is taking an abstract problem and explaining step by step why it is true. Proof based mathematics differs from non-proof based mathematics in many ways. Proof based math deals with using logic while non-proof based math is stra
CSU Channel Islands - MATH - 331
Pythagorean theoremThe concept of proof is an argument that is used to show the truth of a mathematical assertion. In modern mathematics, a proof begins with one or more statements called premises and demonstrates, using the rules of logic, that if
CSU Channel Islands - MATH - 95
Math Lab Syllabus Math 94 and Math 95 Lab assistant: Jaimee Morrison Email: jaimee.morrison191@dolphin.csuci.edu Lab assistant: Melinda Sherman Email: melinda.sherman049@dolphin.csuci.edu Lab hours: Monday OH 1964 1:30-3pm OH 1964 6-8pm Tuesday Wedne
CSU Channel Islands - MATH - 331
Project 1 What exactly is a mathematical proof? The concept of a proof is a way to communicate the steps you have taken to justify why your answer is right or to prove that it is right. I took a Logic class last semester and all we did were proofs. W
CSU Channel Islands - MATH - 331
Project 2 Unquestionably, calculus was the most remarkable mathematical achievement of the seventeenth century because creative mathematics passed to an advanced level. Calculus also led to, essentially, the termination of the history of elementary m
CSU Channel Islands - MATH - 331
Project OneA proof is a way of showing why an equation or a set of steps works and will give the correct answer. It follows through every step showing why each jump of logic is true and valid. Proof based mathematics differ from non-proofed mathema
CSU Channel Islands - MATH - 331
Project 1 History of Math Number: 772 In mathematics, a proof is a formalized, expository technique for demonstrating the validityor invalidityof a proposition. As such, proofs rely upon detailed, logical steps that can not only be followed by the re
CSU Channel Islands - MATH - 331
#380 Math 331 Project 2 European Mathematics began to develop after the fall of the Roman Empire. Three main mathematicians during the Dark Ages were: Boethius of Rome, Bede and Alcuin of Britain, and Gerbert of France. Boethius incorporated statemen